Tips my old coach (a former European pro) taught me to get a faster avg. speed:
1. Ride more in the drops. Most of the guys I ride with are rarely if ever in the drops. I try to spend at least half of every ride in the drops. Get used to it and stay low, it reduces wind resistance and optimizes hip angle.
2. Learn to ride "smoothly". Constant acceleration/deceleration is exhausting and counter-productive. Stay seated as much as possible, don't stomp on the pedals. Think "circles" as you pedal. Use the terrain: work the hills and then get rest on descents.
3. Use your gears. I see a lot of guys who never shift. In rolling terrain, you should be constantly shifting to optimize cadence and keep things efficient.
4. Intervals are the best way to train yourself to go faster. I do sets of 90 seconds on, 30 seconds off. Really work them. Do both hill and flat intervals. "Fartlek"-style training is also hugely helpful in training yourself to effectively bridge gaps and deal with pace changes.
5. Ride with people who are slightly faster than you or more experienced. Shift when they do, note the details of how they pedal and their positioning and copy them.